eBook ISBN:  9781470458409 
Product Code:  DOL/17.E 
List Price:  $35.00 
MAA Member Price:  $26.25 
AMS Member Price:  $26.25 
eBook ISBN:  9781470458409 
Product Code:  DOL/17.E 
List Price:  $35.00 
MAA Member Price:  $26.25 
AMS Member Price:  $26.25 

Book DetailsDolciani Mathematical ExpositionsVolume: 17; 1996; 257 ppMSC: Primary 00
Ross Honsberger's love of mathematics comes through very clearly in From Erdös to Kiev. He presents intriguing, stimulating problems that can be solved with elementary mathematical techniques. It will give pleasure to motivated students and their teachers, but it will also appeal to anyone who enjoys a mathematical challenge. Most of the problems in the collection have appeared on national or international Olympiads or other contests. Thus, they are quite challenging (with solutions that are all the more rewarding). The solutions use straightforward arguments from elementary mathematics (often not very technical arguments) with only the occasional foray into sophisticated or advanced ideas. Anyone familiar with elementary mathematics can appreciate a large part of the book. The problems included in this collection are taken from geometry, number theory, probability, and combinatorics. Solutions to the problems are included.

Table of Contents

Chapters

Seven Solutions by George Evagelopoulos

A Decomposition of a Triangle

AIME—1987

A Problem from the 1991 AIME Examination

Nine Unused Problems from the 1987 International Olympiad

Two Problems from the 1988 USA Olymiad

From the 1988 International Olympiad

A Geometric Gem of Duane DeTemple

A Key Olympiad Problem

Some Student Favorites

Four Unused Problems from the 1988 International Olympiad

From the 1988 AIME Examination

An Unused Bulgarian Problem on the Medial Triangle and the Gergonne Triangle

Two Solutions by John Morvay from the 1982 Leningrad High School Olympiad

Two Solutions by Ed Doolittle

From the 1987 Spanish Olympiad

A Problem from Johann Walter

From the 1987 Balkan Olympiad

From Various Kürschák Competitions

Two Questions from the 1986 National Junior High School Mathematics Competition of the People’s Republic of China

From the 1986 Spanish Olympiad

A Geometric Construction

An Inequality Involving Logarithms

On Isosceles RightAngled Pedal Triangles

Two Problems from the 1987 Austrian Olympiad

From the 1988 Canadian Olympiad

A Problem on Closed Sets

From the 1987 AustrianPolish Team Competition

Two Problems from the AustrianPolish Mathematics Competition

An Engaging Property Concerning the Incircle of a Triangle

On Floors and Ceilings

Two Problems from the 1987 International Olympiad

On Arithmetic Progressions

A Property of Triangles Having an Angle of 30$^\circ $

From the 1985 Bulgarian Spring Competition

An Unused International Olympiad Problem from Britain

A Rumanian Olympiad Proposal

From the 1984 Bulgarian Olympiad

Two Erdös Problems

From the 1985 Bulgarian Olympiad

From a Chinese Contest

A Japanese Temple Geometry Problem

Two Problems from the Second Balkan Olympiad, 1985

A Property of Pedal Triangles

Three More Solutions by George Evagelopoulos

The Power Mean Inequality


Reviews

'Ross Honsberger's love of mathematics comes through very clearly in From Erdős to Kiev. He presents intriguing, stimulating problems that can be solved with elementary mathematical techniques. It will give pleasure to motivated students and their teachers, but will also appeal to anyone who enjoys a mathematical challenge.'
L'Enseignement Mathematique 
'The publication of every new volume in The Dolciani Mathematical Expositions of the Mathematical Association of America is an important event ... This book is recommended to teachers, students and everyone, who enjoy the fun and games of problem solving and have the opinion that asking and answering problems is what keeps a mathematician young in spirit.'
Acta. Sci. Math.


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
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 Reviews
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Ross Honsberger's love of mathematics comes through very clearly in From Erdös to Kiev. He presents intriguing, stimulating problems that can be solved with elementary mathematical techniques. It will give pleasure to motivated students and their teachers, but it will also appeal to anyone who enjoys a mathematical challenge. Most of the problems in the collection have appeared on national or international Olympiads or other contests. Thus, they are quite challenging (with solutions that are all the more rewarding). The solutions use straightforward arguments from elementary mathematics (often not very technical arguments) with only the occasional foray into sophisticated or advanced ideas. Anyone familiar with elementary mathematics can appreciate a large part of the book. The problems included in this collection are taken from geometry, number theory, probability, and combinatorics. Solutions to the problems are included.

Chapters

Seven Solutions by George Evagelopoulos

A Decomposition of a Triangle

AIME—1987

A Problem from the 1991 AIME Examination

Nine Unused Problems from the 1987 International Olympiad

Two Problems from the 1988 USA Olymiad

From the 1988 International Olympiad

A Geometric Gem of Duane DeTemple

A Key Olympiad Problem

Some Student Favorites

Four Unused Problems from the 1988 International Olympiad

From the 1988 AIME Examination

An Unused Bulgarian Problem on the Medial Triangle and the Gergonne Triangle

Two Solutions by John Morvay from the 1982 Leningrad High School Olympiad

Two Solutions by Ed Doolittle

From the 1987 Spanish Olympiad

A Problem from Johann Walter

From the 1987 Balkan Olympiad

From Various Kürschák Competitions

Two Questions from the 1986 National Junior High School Mathematics Competition of the People’s Republic of China

From the 1986 Spanish Olympiad

A Geometric Construction

An Inequality Involving Logarithms

On Isosceles RightAngled Pedal Triangles

Two Problems from the 1987 Austrian Olympiad

From the 1988 Canadian Olympiad

A Problem on Closed Sets

From the 1987 AustrianPolish Team Competition

Two Problems from the AustrianPolish Mathematics Competition

An Engaging Property Concerning the Incircle of a Triangle

On Floors and Ceilings

Two Problems from the 1987 International Olympiad

On Arithmetic Progressions

A Property of Triangles Having an Angle of 30$^\circ $

From the 1985 Bulgarian Spring Competition

An Unused International Olympiad Problem from Britain

A Rumanian Olympiad Proposal

From the 1984 Bulgarian Olympiad

Two Erdös Problems

From the 1985 Bulgarian Olympiad

From a Chinese Contest

A Japanese Temple Geometry Problem

Two Problems from the Second Balkan Olympiad, 1985

A Property of Pedal Triangles

Three More Solutions by George Evagelopoulos

The Power Mean Inequality

'Ross Honsberger's love of mathematics comes through very clearly in From Erdős to Kiev. He presents intriguing, stimulating problems that can be solved with elementary mathematical techniques. It will give pleasure to motivated students and their teachers, but will also appeal to anyone who enjoys a mathematical challenge.'
L'Enseignement Mathematique 
'The publication of every new volume in The Dolciani Mathematical Expositions of the Mathematical Association of America is an important event ... This book is recommended to teachers, students and everyone, who enjoy the fun and games of problem solving and have the opinion that asking and answering problems is what keeps a mathematician young in spirit.'
Acta. Sci. Math.